Later Thursday, the Senate confirmed Burwell to replace outgoing HHS Secretary Kathleen Sebelius in a 78-17 vote. More than 20 Republicans joined Democrats in voting for her, while others in the GOP, such as McConnell, voted no.

Burwell’s major task will be the implementation of the healthcare law — an effort that McConnell said is doomed to failure.

“The Senate will vote on President Obama’s newest choice to head the Department of Health and Human Services. In other words, the person he’ll be sticking with the impossible task of trying to make ObamaCare work,” McConnell said. “In my view, the Senate shouldn’t be focusing on a new captain for the Titanic. It should focus on steering away from the iceberg.”

On Wednesday, the Senate easily advanced Burwell’s nomination in a 67-28 vote, with 14 Republicans joining Democrats to end debate.

Burwell was unanimously confirmed to her current role as director of the Office of Management and Budget.

But some Republicans have said they'd still oppose her nomination as a protest against ObamaCare.

“She’ll be the Chief Operating Officer of ObamaCare implementation — a law that’s doing incredible damage to middle-class families in this country,” McConnell said. “And her embrace of this disastrous law is reason enough to oppose her confirmation.”

McConnell is facing a tough reelection race in November and has been an ardent critic of ObamaCare.